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Standard XII

Physics

Deducing Mathematically

A rigid body ...

Question

A rigid body rotates about a stationary axis with an angular retardation $α = 4 \sqrt{ω}$ , where $ω$ is the angular speed of the body. Find the time after which the body will come to rest, if initially it was rotating at an angular speed of 9 rad/sec.

t = 3 s e c

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t = \frac{3}{2} s e c

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t = 12 s e c

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t = 4 \sqrt{3} s e c

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Solution

The correct option is B $t = \frac{3}{2} s e c$
$A n g u l a r a c c e l e r a t i o n, α = - 4 \sqrt{ω} = \frac{d ω}{d t} \int_{9}^{0} \frac{d ω}{\sqrt{ω}} = - \int_{0}^{t} 4 d t {(\frac{ω^{- \frac{1}{2} + 1}}{^{- \frac{1}{2} + 1}}]}_{9}^{0} = - {(4 t]}_{0}^{t} \Rightarrow {(2 \sqrt{ω}]}_{9}^{0} = - 4 t 2 ⎛ ⎜ ⎝ - 3 ⎞ ⎟ ⎠ = - 4 t \Rightarrow t = \frac{3}{2} s e c$

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A rigid body rotates about a stationary axis with an angular retardation α=4√ω, where ω is the angular speed of the body. Find the time after which the body will come to rest, if initially it was rotating at an angular speed of 9 rad/sec.

The correct option is B t=32secAngular acceleration, α=−4√ω=dωdt∫09dω√ω=−∫t04dt(ω−12+1−12+1]09=−(4t]t0⇒(2√ω]09=−4t2⎛⎜⎝−3⎞⎟⎠=−4t⇒t=32 sec

A rigid body rotates about a stationary axis with an angular retardation $α = 4 \sqrt{ω}$ , where $ω$ is the angular speed of the body. Find the time after which the body will come to rest, if initially it was rotating at an angular speed of 9 rad/sec.